SOLUTION: OK now i have a question that i TOTALLY don't get. Its how do you find the arc length and area of a sector with the given..... r=2cm, and the weird 0 with the slash through it =9PI

Algebra ->  Trigonometry-basics -> SOLUTION: OK now i have a question that i TOTALLY don't get. Its how do you find the arc length and area of a sector with the given..... r=2cm, and the weird 0 with the slash through it =9PI      Log On


   

Question 74773This question is from textbook
: OK now i have a question that i TOTALLY don't get. Its how do you find the arc length and area of a sector with the given..... r=2cm, and the weird 0 with the slash through it =9PI/20 Please help!!! This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The reason why radians are used is because with a unit circle the angle measure is the arc length. So if I have an angle with the measure of pi, then I have an arc length of pi. So the arc length formula of a unit circle is

So if we have a circle with a radius of 2, we just multiply the formula by 2.

For a general radius r we have

So for a radius of 2 cm and an angle of the arc length is:


So the arc length is




To find the area of a circle, the formula is given as:

So to find the area of a sector, we just multiply this total area by a fraction. For instance, if we have half a circle (with an angle of pi) we multiply the total area by 1/2.



For any general we do the same thing


So the area of a sector is

So lets plug in r=2 and


So the area is